All three games between the two sides had finished as draws last season and it looked set to be another stalemate until Burnley stepped up the pace in the final third of the match.
In the third minute, Southampton created the first opening but Che Adams, a summer signing from Birmingham City, failed to turn Yan Valery's cross goalwards.
After Clarets striker Chris Wood had rightly seen his effort disallowed for offside, Johann Berg Gudmundssons shot from the edge of the penalty area flew narrowly wide.
Adams was a little fortunate not be sent off for a nasty challenge on Ben Mee before Nathan Redmond went close to breaking the deadlock just before half-time, only for his shot to fly over Nick Popes goal.
After a dreary first 45 minutes, the second period began with a bit more activity. Redmond was brought down just outside the area by James Tarkowski. Ryan Bertrand took the resulting free-kick, but was unable to test Pope with his effort.
Redmond then curled a shot over the bar from a promising position, but it was the Clarets who grabbed the opener in the 63rd minute, Ashley Barnes showing great control before slotting a low drive past Angus Gunn in the Southampton goal.
Just seven minutes later, Sean Dyches side doubled their lead when Barnes crashed a shot home after latching on to Erik Pieters cross. Gudmundsson added a third goal in the 75th minute when he curled a fine shot past Gunn to finally sink a disappointing Saints side.